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We extend the definition of \[Gamma] to allow for multiples indices. \
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Cell["\<\
The following code for the irreducible decomposition in antisymmetric \
\[Gamma] is adapted from GAMMA.m package (using Jose and Alfonso\
\[CloseCurlyQuote]s code). 
Initially there were three parts in this GAMMA.m code
\t1) decomposition of a product of gammas into irreducible parts (deltas and \
antisymmetrized gammas),
\t2) contraction of indices in two **contiguous** gammas in a product,
\t3) computation of traces.\t
Here we report **ONLY** the 1), that is the decomposition in irreducible \
components.\
\>", "Text"],

Cell["\<\
Wrapping function that performs the irreducible decomposition (the essential \
of the code is in the function GE implemented below).\
\>", "Text"],

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Common code: a numerical factor and the key algorithm for expansion of a \
product of two antisymmetrized gammas. Note that Gran\[CloseCurlyQuote]s \
Delta with two p-blocks is our Gdelta/p!, and hence the following factor does \
not have a p! multiplying in the numerator, that Gran has.\
\>", "Text"],

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Cyril TODO Careful that if the user uses the index ' p' then it conflicts \
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Let us check the irreducible decomposition on some simple operations\
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When we add a \[Gamma]hat at the end of the product of \[Gamma] matrices, the \
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Some examples of Canonicalization according to the symmetries\
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This functions replaces the non-vanishing Traces of products by a tensor with \
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End values of the recursion. 
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There is a slower but more general method which does not break the symmetry \
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We define a function which uses all these rules to remove the traces\
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     AutoSpacing->False],
    $CellContext`P2[$CellContext`j],
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   InterpretationBox[
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        StyleBox[GridBox[{
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           {"i"}
          },
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          Offset[0.2]}, "RowsIndexed" -> {}}],
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     AutoSpacing->False],
    $CellContext`P3[-$CellContext`i],
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   InterpretationBox[
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       {"P4", 
        StyleBox[GridBox[{
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           {"j"}
          },
          GridBoxSpacings->{"Columns" -> {
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        "RowsIndexed" -> {}},
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           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
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     AutoSpacing->False],
    $CellContext`P4[-$CellContext`j],
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}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1304, 723},
WindowMargins->{{198, Automatic}, {Automatic, 151}},
FrontEndVersion->"10.4 for Mac OS X x86 (32-bit, 64-bit Kernel) (April 11, \
2016)",
StyleDefinitions->"Default.nb"
]

